Highest Common Factor of 416, 582, 291 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 416, 582, 291 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 416, 582, 291 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 416, 582, 291 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 416, 582, 291 is 1.
HCF(416, 582, 291) = 1
HCF of 416, 582, 291 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 416, 582, 291 is 1.
Highest Common Factor of 416,582,291 is 1
Step 1: Since 582 > 416, we apply the division lemma to 582 and 416, to get
582 = 416 x 1 + 166
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 166 and 416, to get
416 = 166 x 2 + 84
Step 3: We consider the new divisor 166 and the new remainder 84, and apply the division lemma to get
166 = 84 x 1 + 82
We consider the new divisor 84 and the new remainder 82,and apply the division lemma to get
84 = 82 x 1 + 2
We consider the new divisor 82 and the new remainder 2,and apply the division lemma to get
82 = 2 x 41 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 416 and 582 is 2
Notice that 2 = HCF(82,2) = HCF(84,82) = HCF(166,84) = HCF(416,166) = HCF(582,416) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 291 > 2, we apply the division lemma to 291 and 2, to get
291 = 2 x 145 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 291 is 1
Notice that 1 = HCF(2,1) = HCF(291,2) .
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Frequently Asked Questions on HCF of 416, 582, 291 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 416, 582, 291?
Answer: HCF of 416, 582, 291 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 416, 582, 291 using Euclid's Algorithm?
Answer: For arbitrary numbers 416, 582, 291 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.